Given Information:
Number of lithium batteries = n = 16
Mean life of lithium batteries = μ = 645 hours
Standard deviation of lithium batteries = σ = 31 hours
Confidence level = 95%
Required Information:
Confidence Interval = ?
Answer:
[tex]CI = 628.5 \: to \: 661.5 \: hours[/tex]
Step-by-step explanation:
The confidence interval is given by
[tex]CI = \mu \pm t_{\alpha/2} (\frac{\sigma}{\sqrt{n}})[/tex]
Where μ is the mean life of lithium batteries, σ is the standard deviation, n is number of lithium batteries selected, and t is the critical value from the t-table with significance level of
tα/2 = (1 - 0.95) = 0.05/2 = 0.025
and the degree of freedom is
DoF = n - 1 = 16 - 1 = 15
The critical value (tα/2) at 15 DoF is equal to 2.131 (from the t-table)
[tex]CI = 645 \pm 2.131(\frac{31}{\sqrt{16}})[/tex]
[tex]CI = 645 \pm 2.131(7.75})[/tex]
[tex]CI = 645 \pm 16.515[/tex]
[tex]CI = 645 - 16.515 \: and \: 645 + 16.515[/tex]
[tex]CI = 628.5 \: to \: 661.5 \: hours[/tex]
Therefore, the 95% confidence interval is 628.5 to 661.5 hours
What does it mean?
It means that we are 95% confident that the mean life of 16 lithium batteries is within the interval of (628.5 to 661.5 hours)
Suppose 80% of people enjoy swimming. Suppose 70% of people enjoy running.
Suppose 55% of people enjoy doing both. What percentage of people enjoy swimming
and/or running?
Answer:
95%
Step-by-step explanation:
In this case we can apply a formula that tells us that:
# (AUB) = #A + #B - #AnB
Where A would be the ones who enjoy swimming and B would be the ones who enjoy running. AnB is the intersection of both sets, that is, those who enjoy doing both things, these values we have, if we replace them we have left:
#(AUB) = 80% + 70% - 55%
#(AUB) = 95%
Which means that 95% of people enjoy either swimming or running
The percentage of people who enjoy swimming and/or running is calculated to be 95%.
We have 80% of people who enjoy swimming, and 70% who enjoy running, with a 55% overlap of people who enjoy both.
The formula for the principle of inclusion-exclusion is:
Union = A + B - Intersection
Therefore, the percentage of people who enjoy swimming and/or running is:
Union = 80% + 70% - 55% = 95%
Hence, 95% of people enjoy at least one of the two activities.
what is the answer pls
Given:
Surface area = 4,362 yards
Length = 36 yard
Width = 21 yard
Height = c
To find:
Volume of the rectangular prism.
Solution:
Surface area formula:
[tex]SA = 2(lw+wh+lh)[/tex]
Substitute the given values.
[tex]4362 = 2(36\times21 +21 \times c+36 \times c)[/tex]
[tex]4362 = 2(756+21 c+36 c)[/tex]
[tex]4362 = 2(756+57c)[/tex]
[tex]4362 = 1512+114c[/tex]
Subtract 1512 from both sides.
[tex]4362- 1512 = 1512+114c - 1512[/tex]
[tex]2850=114c[/tex]
Divide by 114 on both sides, we get
25 = c
Height = 25
Volume = length × breadth × height
= 36 × 21 × 25
= 18900
Volume of rectangular prism is 18900 cubic yards.
ms.roa pays the same amount each month for internet service she is making a graph to show the amount she pays over time. Please help
Answer:
Step-by-step explanation:
Ms. Roa's monthly internet payment, being constant, would be represented by a horizontal line on a graph with time (months) on the X-axis and cost on the Y-axis. The consistency of the payment amount regardless of time represents a constant rate, demonstrated graphically.
Explanation:The subject of your question involves mathematics, specifically, the concept of the relationship between constant costs and time, which can be demonstrated using linear graphs. In Ms. Roa's case, she pays the same amount each month for internet service. This means that the cost per month is constant, so if you make a graph showing time on the X axis (in months) and cost on the Y axis, you would see a straight horizontal line, indicating that the cost does not change over time.
For example, if Ms. Roa pays $50 each month, then every point on the line will be at Y = 50 (for cost), regardless of the X value (time). The concept of a constant rate is important in understanding the relationship between different quantities, and is commonly used in Displaying Data Graphically and Interpreting the Graph.
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HELP NEEDED !!! PLEASE
The external angles of a 12-gon add up to 360 degrees so each is 30 degrees. That makes the internal angle the supplement, PQR=150 degrees.
We have an isosceles triangle so the other two angles add to 30 degrees, so 15 degrees.
Answer: 15 degrees
Angle PRO in a regular 12-gon is half an interior angle, so it measures [tex]$\boxed{75^\circ}$[/tex].
The strategy is to first calculate the sum of the interior angles of the dodecagon, and then divide that number by 2 because any angle of a regular polygon can be found by subtracting [tex]$180^\circ$[/tex] from the quotient you get when you divide the sum of the interior angles by the number of angles.
Here's the solution:
The sum of the interior angles of a polygon is given by the formula [tex]$(n-2)\times180^\circ$[/tex], where n is the number of sides.In a dodecagon, there are n=12 sides.Therefore, the sum of the interior angles of the dodecagon is [tex]$(12-2)\times180^\circ = 1800^\circ$[/tex].Since each angle of a regular polygon is equal, all the interior angles of the dodecagon measure [tex]$\frac{1800^\circ}{12} = 150^\circ$[/tex]Since [tex]$\angle PRO$[/tex] is half of an interior angle of the dodecagon, it measures [tex]$\frac{1}{2}\times150^\circ = \boxed{75^\circ}$[/tex].If a single 9-sided die is tossed once, find the probability of rolling a number greater than 7.
The probability of rolling a number greater than 7 is
(Simplify your answer.)
Answer:
[see explanation]
Step-by-step explanation:
There are 9 numbers on the dice. (One number for each side.)
Total Number of events: 9
There are 2 numbers that are greater than seven. (8 and 9)
Preferred number of events: 2
[tex]\frac{preferred}{total} =\frac{2}{9}[/tex]
[tex]\frac{2}{9}[/tex] is already at it's lowest terms.
The probability should be 2/9.
The probability of rolling a number greater than 7 on a 9-sided die is 2/9 or approximately 22.2%.
Explanation:In the language of probability, an event is any outcome or combination of outcomes. The probability of any event is normally calculated by dividing the number of ways that the event can occur by the total number of outcomes. In this problem, a die with 9 sides is rolled once, giving a total of 9 possible outcomes (the numbers 1 to 9). The event in question is rolling a number greater than 7, which consists of two outcomes: 8 and 9. So, the probability of this event is
Number of ways the event can occur / Total number of outcomes = 2 / 9 = 0.222 (to three decimal places), or approximately 22.2%.
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Please help me with this question thank you
Given:
Deposit = $7500
Rate of interest = 2.75%
Time = 4 years
Compounded monthly
n = 12
To find:
The balance in the account after 4 years
Solution:
Compound interest formula:
[tex]$A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
Here P = $7500, r = 2.75%, n = 12 and t = 4.
[tex]$A=7500\left(1+\frac{2.75\%}{12}\right)^{12\times 4}[/tex]
To convert percentage into fraction, divide by 100.
[tex]$A=7500\left(1+\frac{\frac{2.75}{100} }{12}\right)^{48}[/tex]
[tex]$A=7500\left(1+\frac{0.0275 }{12}\right)^{48}[/tex]
[tex]$A=7500\left(\frac{12+0.0275 }{12}\right)^{48}[/tex]
[tex]$A=7500\left(\frac{12.0275 }{12}\right)^{48}[/tex]
[tex]$A=8371.03[/tex]
The balance in his account after 4 years is $8371.03.
In the diagram, point B is a point of tangency.Find the radius r of this diragram . THANKY YOU
Answer:
r= 18
Step-by-step explanation:
use the Pythagorean theorem to solve this
[tex]r^{2} +24^{2} =(r+12)^{2}[/tex]
[tex]r^{2}+576=r^{2} +24r+144[/tex]
-144 -144
[tex]r^{2}+432=r^{2} +24r[/tex]
-[tex]r^{2}[/tex] -[tex]r^{2}[/tex]
[tex]432=24r[/tex]
/24 /24
18=r
Angle 1 and angle 2 are what kind of angles?
Answer:
supplementary angles
Step-by-step explanation:
one angle is an obtuse angle
and another angle is an acute angel.
2n + 4n = 42
Answer: the value of n is .....
Answer:
7
Step-by-step explanation:
2n + 4n = 6n, adding like terms
6n = 42
6n/6 = 42/6
n = 7
Answer: 7
Step-by-step explanation:
4x7= 28 and 2x7=14
14+28= 42
Kimani ordered party hats for his son's birthday party and
spent over $40. If he ordered the hats from Party Plus, write
an inequality to represent the possible number of hats he
ordered.
The inequality representing the possible number of party hats (x) Kimani ordered from Party Plus is x>20. This means Kimani ordered more than 20 party hats to spend over $40, given the assumed minimum cost per hat from Party Plus.
Let's denote the number of party hats Kimani ordered from Party Plus as x. Now, if each party hat costs a certain amount, and Kimani spent over $40, we can set up an inequality to represent this situation.
Let be the cost of each party hat. The total cost (T) is given by multiplying the number of hats (x) by the cost per hat (c). Therefore, T=xc.
The problem states that Kimani spent over $40, so we can express this as an inequality: T>40
Now, substitute the expression for T in terms of x and xc>40
Since we are specifically looking at the scenario where Kimani ordered the hats from Party Plus, let's assume that each hat costs at least $2 (as a hypothetical example). So, c≥2. Now, substitute
c≥2 into the inequality:
x⋅2>40
Simplify the inequality:
2x>40
Now, divide both sides by 2 to solve for x>20.
What is the radius of a hemisphere with a volume of 60,750π cm3?
The radius of the hemisphere is 45 cm
Explanation:
Given:
Volume of the hemisphere, V = 60750π cm³
Radius of the hemisphere, r = ?
We know:
Volume of hemisphere = [tex]\frac{2\pi r^3 }{3}[/tex]
[tex]60750\pi = \frac{2\pi r^3 }{3} \\\\r^3 = 91125\\\\r = 45[/tex]
Therefore, the radius of the hemisphere is 45 cm
The radius of the hemisphere is 45 cm
The volume of a hemisphere is given by the formula
[tex]V = \frac{2}{3} \pi r^{3}[/tex]
Where V is the volume
and r is the radius
From the question,
V = 60750π cm³
Putting this into the formula,
We get
[tex]60750\pi = \frac{2}{3}\pi r^{3}[/tex]
∴ [tex]r^{3}= \frac{60750\pi \times 3}{2\pi}[/tex]
[tex]r^{3}= 91125[/tex]
∴ [tex]r =\sqrt[3]{91125}[/tex]
r = 45 cm
Hence, the radius of the hemisphere is 45 cm
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57:23
The two-way table shows the ages of the players on different soccer teams.
Team A
4
Team D
3
8 Years Old
9 Years Old
| 10 Years Old
Total
Team B Team C
6
8
4
3
35
13
16
Total
21
23
14
58
Which statement is true?
The probability that a randomly selected player on Team A is 8 years old is 4
The probability that a randomly selected 8-year-old player is on Team C is 16
The probability that a randomly selected player on Team C is 10 years o
The probability that a randomly selected 10-year-old player is on Team Bi
Save and Exit
Mark this and return
Submit
Next
Answer: 5/16
Step-by-step explanation:
i just took the test
The answer is C. The probability that a randomly selected player on Team C is 10 years old is 5/16.
Good luck :)
10. The population of a small town was 3600 in 2005. The population increases by 4% annually.
Answer:
The growth function:
y=3600(1.04)^t
The population in 2025:
7,888
Step-by-step explanation:
I'm not sure if this is what you asked for, but I did this in my class with my teacher (algebra)
Luke has 22 lots for sale. Each lot is 1.63 acres. How much land does Luke have for sale?
OA 37.49 acres
OB. 36.76 acres
OC. 35.86 acres
OD 38.06 acres
Answer: 35.86acres
Step-by-step explanation:
Luke has 22lots for sale
Each lot is 1.63acres
Since each lot is 1.63acres and there are 22lots
So Luke has
22×1.63acres
=35.86acres
Final answer:
Luke has 35.86 acres of land for sale, which is the product of multiplying 22 lots by 1.63 acres per lot.
Explanation:
To calculate the total amount of land Luke has for sale, multiply the number of lots by the acreage of each lot. There are 22 lots for sale, and each lot measures 1.63 acres. The calculation is as follows:
Total land = Number of lots * Acreage of each lot
Total land = 22 * 1.63
Total land = 35.86 acres
So, Luke has a total of 35.86 acres of land for sale, which corresponds to option OC.
. My best friends and I met at the movies at
6:45pm. We were picked up at 8:15pm. How
long were we at the movies?
Answer:
1 hour and 30 minutes
Step-by-step explanation:
Answer:
the answer to this is 1 hour and 30 minutes
Step-by-step explanation:
my exlanation is one hour from 6:45 is 7:45 15 minutes until 8:00 then 15 more minute until she gets picked up. I HOPE THIS HELPS AND PLZ AND KINDLEY MARK ME BRAINLIEST HAVE A GOOD REST OF YOUR DAY =)
SOMEONE PLEASE HELP MEEEEEEEEEEEEEEEEEE
Answer:
y = -(5/2)x - 1
Step-by-step explanation:
slope intercept form is y = mx + b
m is the slope
b is the y intercept
The y intercept is shown to be (0,-1), so b = -1
The equation is now y = mx -1
slope= rise/run
The rise is (4-(-1))=5
The run is (-2-0)=-2
5/-2 is the slope (m)
The equation is y = -(5/2)x - 1
Answer:
y = -5/2 x-1
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (-1 -4)/(0--2)
= (-5)/+2
= -5/2
We know the y intercept is -1 since that is where it crosses the y axis
We will use the slope intercept form of the equation
y= mx+b where m is the slope and b is the y intercept
y = -5/2 x-1
A rotation of 150° counterclockwise about the origin would be the same as a rotation of__________ clockwise about the origin.
360°
300°
30°
210°
Answer:
210
Step-by-step explanation:
360-150
think about it like going the opposite direction on a circle.
if you are on a 1 mile trail that is a circle at the starting point and you walk right to get to a marker that is half way, if you went left, the marker would be 0.5 miles the opposite direction.
Which of the following expressions are equivalent to -5.93 + (-8.62) + 5.93?
Choose 4 answers.
a. -8.62
b. −5.93 − (8.62−5.93)
c. −(5.93 + 8.62) + 5.93
d. -5.93 - 8.62 - (-5.93)
e. -5.93 − (8.62 + 5.93)
Answer:
A, B, C & D
Step-by-step explanation:
Expand and see which is is equivalent to the given expression.
what equation matches the table?
Answer:
C ; y =3x
Step-by-step explanation:
if you look at the function table
it goes like this
1 to 3
2 to 6
3 to 9
1*3=3
2*3=6
3*3=9
please thank me, rate, and mark brainliest if you like!
;)
Answer:
C
Step-by-step explanation:
The x values are multiplying themselves by 3 to get the y values
What’s the answer I don’t get this
Answer:
K(-1)=6
Step-by-step explanation:
t=-1
2 times -1 squared
-1 squared=1
2x1 = 2
2+4=6
K(-1)=6
Create a cylinder with a height of 8 cm and a radius of 4
cm. Make note of the volume.
Which could you do to increase the volume? Check all
that apply.
Double the height
Double the radius
Double the height but half the radius.
Double the radius but half the height.
Make the radius and height both 6 cm.
Answer: The volume is 128pi cm or 402.12 cm. To increase the volume you can double the height, double the radius, double the radius but half the height, and make the radius and height both 6 cm.
Step-by-step explanation:
To find the volume of the cylinder, use the equation [tex]\pi r^2h[/tex]. After plugging everything in, the equation is [tex]\pi (4^2)*8[/tex]. [tex]4^2[/tex]=16. 16*8=128. If you need a more accurate answer, multiply by pi to get 402.12 cm.
Doubling the height creates a volume of 256pi cm.
Doubling the radius creates a volume of 512pi cm.
Doubling the radius and halving the height creates a volume of 256pi cm.
Making both the radius and height 6 cm creates a volume of 216pi cm.
Answer:
1, 2, 4, 5
Step-by-step explanation:
your welcome.
Simplify by combining like terms: -3 + 6x - 18 - 22x *
Answer:
-21 -16x
Step-by-step explanation:
-3 + 6x - 18 - 22x
Combine like terms
-3 -18 +6x -22x
-21 -16x
Answer:
-21-16x
Step-by-step explanation:
There are 850 employees at a software company. The company’s CEO was interested in finding out if his employees prefer the new coffee brand provided in the break rooms or the old coffee brand.
A random sample of 200 employees was conducted, and 148 employees said that they prefer the new coffee brand over the old one.
The point estimate is calculated using the formula = .
Which statements are true about estimating the population proportion of employees who prefer the new coffee brand? Check all that apply.
Answer: B & E
i just took it
Step-by-step explanation:
Answer:
the answer is B and E
Step-by-step explanation:
I just took it on edg
In triangle abc, AC=15 BC=11 and m
Answer: 10
Step-by-step explanation:
In a right angle triangle
Hypothenus ^2= opposite ^2+ adjacent ^2
According to a diagram below
Hypothenus =15
Opposite =?
Adjacent =11
Substitute for the values
15^2=11^2+opp^2
Opp^2=15^2-11^2
0pp^2= 225-121
Opp2=104
Opp= square root of 104
Opp= 10.2
Opp= ~10
Simple solutions grade 7 answer key
The Simple Solutions Grade 7 answer key is a resource for middle school students to check their math work and learn from their mistakes.
Explanation:The Simple Solutions Grade 7 answer key is a resource that provides answers and explanations for the Simple Solutions Mathematics program for middle school students. It is designed to help students understand and practice the math concepts they are learning in class.
This answer key can be used by students to check their work, verify their answers, and learn from any mistakes they may have made.
Using the Simple Solutions answer key can also help students track their progress and identify areas where they may need additional practice or support.
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Solve for x: 3x - 4 = 23
Answer: x =
Answer:
x = 9
Step-by-step explanation:
3x - 4= 23
3x-4+4 + 23+4
3x + 27
3x/3 + 27/3
x+ 9
The solution of expression 3x - 4 = 23 is by combining the like terms with the help of operations such as addition, subtraction, etc would be,
x = 9
Given that,
The expression is,
3x - 4 = 23
Used the concept of expression by combining the like terms with the help of operations such as addition, subtraction, etc.
Here the expression is,
3x - 4 = 23
Add 4 on both sides,
3x - 4 + 4 = 23 + 4
3x = 27
Divide by 3 on both sides,
x = 27/3
Therefore, the solution is,
x = 9
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Consider the reduction of the complex figure with a scale factor of 1
7
. What is the area of the reduced figure?
A large complex figure with 5 sides has a left side length of 28 millimeters and top side length of 42 millimeters. The area is 1225 millimeters squared. A smaller complex figure with 5 sides has a left side length of 4 millimeters and top side length of 6 millimeters.
mm2
25 cause when i put in the answer it was right
Answer:
its a on edg
Step-by-step explanation:
Celine flipped a coin 100 times. She flipped heads 41 times and tails 59 times. What is the experimental probability that the next flip will be heads?
A - 41/100
B - 1/2
C - 3/4
D - 59/100
Answer:
B - 1/2
Step-by-step explanation:
In this situation each experiment does not affect the probability of the next one. That is, each experiment is independent of the rest. Hence, independently of the result of the first 100 times the next probability in which Celine does the experiment, the propability will be 1/2.
B - 1/2
Answer:
B- 41/100
Step-by-step explanation:
Because this is an experimental (not theoretical) probability, which is the ratio of number of outcome as head over the total number of trial, the experimental probability of the next flipping be head would be the total number of heads that she'd gotten before over the total number of times that she'd try, which is 41 / 100
Evaluate the expression 2x+1 , if X=4
Give the correct answer, please!!!!!!!!!!!
Answer:
9
Step-by-step explanation:
if x= 4; 2x+1
2(4) + 1
8 + 1
9
What is the nth term rule of the linear sequence below?
1
,
7
,
13
,
19
,
25
Answer:
[tex]a_{n}[/tex] = 6n - 5
Step-by-step explanation:
There is a common difference d between the consecutive terms, that is
d =7 - 1 = 13 - 7 = 19 - 13 = 25 - 19 = 6
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 1 and d = 6, thus
[tex]a_{n}[/tex] = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5
Answer:
Step-by-step explanation:
t1 = 1 = 6 * 1 - 5
t2 =7 = 6 * 2 - 5
t3 = 13 = 6 * 3 - 5
t4 = 19 = 6*4 - 5
t5 = 25 = 6*5 - 5
-------------------------
Tn = 6n - 5
Hope it helped :)